Question

the length of a rectangle is 5 cm more than its breadth find the dimensions of the rectangle if the perimeter is 34 cm

Answer 1

Let the breadth of the rectangle be x

Then length will be x+5

PERIMETER= 2( L+B)

2(x+x+5)

34 = 4x+10

24= 4x

x= 6

Length is 11

breadth= 6

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Answer 2

$\bf{\huge{\underline{\boxed{\rm{\blue{Answer:}}}}}}$

Given:-

• the length of a rectangle is 5 cm more than its breadth
• perimeter of the rectangle is 34cm

To find :-

• dimensions of the rectangle i.e length and breadth of the rectangle.

Solution :-

Let the breadth of the rectangle be x cm

Then as per the condition mentioned in the question,

• the length of a rectangle is 5 cm more than its breadth

Length = x + 5 cm

Perimeter of the rectangle = 2 (l+b)

Length = x + 5 cm

Breadth = x cm

Perimeter = 34cm

Plug the values,

Perimeter = 2 ( x + 5 + x)

34 = 2 ( 2x + 5)

34 = 4x + 10

34 - 10 = 4x

24 = 4x

4x = 24

x = $\bf\large\frac{24}{4}$

$\bf{\large{\underline{\boxed{\rm{\red{x\: =\: 6\:}}}}}}$

Substitute the value of x in length and breadth of the rectangle to find its dimensions.

$\bf{\large{\underline{\boxed{\rm{\pink{Length\:of\:rectangle\: = \:x + 5 = 6 + 5 = 11\:cm}}}}}}$

$\bf{\large{\underline{\boxed{\rm{\green{Breadth\:of\:rectangle \:=\:x\:=6cm}}}}}}$

$\bf{\huge{\underline{\boxed{\mathfrak{\orange{Verification:}}}}}}$

• Perimeter of the rectangle = 34cm
• Length of the rectangle = 11 cm
• Breadth of the rectangle = 6cm

Perimeter of the rectangle = 2(l+b)

=> 34 = 2 (11 + 6)

=> 34 = 2 (17)

=> 34 = 34

LHS = RHS.

Hence verified.